sos_gs_cfp_1st.m

　sos_gs_cfp.m （ここを参照）において，解を 1 次式
　　
とし， （この値が最小値）と与え，凸可解問題を解いている．有限個の LMI に帰着する方法（ここやここを参照）で得られる最小値 より小さいことが確認できる．

実行結果 (gamma = 168) 

>> sos_gs_cfp_1st

-------------------------------------------------------------------------
YALMIP SOS module started...
-------------------------------------------------------------------------
Detected 208 parametric variables and 2 independent variables.
Detected 0 linear inequalities, 0 equality constraints and 0 LMIs.
Using kernel representation (options.sos.model=1).
Initially 2 monomials in R^1
Newton polytope (0 LPs).........Keeping 2 monomials (0.0624sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 2 monomials in R^1
Newton polytope (0 LPs).........Keeping 2 monomials (0sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 2 monomials in R^1
Newton polytope (0 LPs).........Keeping 2 monomials (0sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 3 monomials in R^1
Newton polytope (0 LPs).........Keeping 3 monomials (0sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 2 monomials in R^1
Newton polytope (0 LPs).........Keeping 2 monomials (0sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 2 monomials in R^1
Newton polytope (0 LPs).........Keeping 2 monomials (0sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 5 monomials in R^2
Newton polytope (1 LPs).........Keeping 3 monomials (0.78001sec)
Finding symmetries..............Found no symmetries (0sec)
Initially 3 monomials in R^1
Newton polytope (0 LPs).........Keeping 3 monomials (0sec)
Finding symmetries..............Found no symmetries (0sec)
 
SeDuMi 1.3 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
Put 208 free variables in a quadratic cone
eqs m = 635, order n = 106, dim = 1979, blocks = 10
nnz(A) = 1644 + 0, nnz(ADA) = 209325, nnz(L) = 104980
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            2.09E-001 0.000
  1 : -3.64E-001 1.27E-001 0.000 0.6089 0.9000 0.9000   1.19  1  1  3.7E+000
  2 : -3.71E-001 4.58E-002 0.000 0.3605 0.9000 0.9000   1.25  1  1  1.7E+000
  3 : -1.67E-001 1.43E-002 0.000 0.3117 0.9000 0.9000   1.33  1  1  9.2E-001
  4 : -6.03E-002 3.73E-003 0.000 0.2615 0.9000 0.9000   1.52  1  1  5.5E-001
  5 : -9.23E-003 9.45E-004 0.000 0.2532 0.9000 0.9000   2.17  1  1  3.0E-001
  6 : -1.98E-003 2.33E-004 0.000 0.2468 0.9000 0.9000   1.43  1  1  2.4E-001
  7 : -3.86E-004 4.99E-005 0.000 0.2138 0.9000 0.9000   1.28  1  1  7.9E-002
  8 : -1.70E-004 2.18E-005 0.000 0.4379 0.9000 0.9000   1.05  1  1  3.6E-002
  9 : -1.04E-004 1.11E-005 0.000 0.5067 0.9000 0.9000   0.55  1  1  2.9E-002
 10 : -5.35E-005 4.99E-006 0.000 0.4511 0.9000 0.9000   0.44  1  1  2.0E-002
 11 : -2.57E-005 2.20E-006 0.000 0.4406 0.9000 0.9000   0.32  1  1  1.2E-002
 12 : -9.87E-006 9.16E-007 0.000 0.4164 0.9000 0.9000   0.35  2  2  6.4E-003
 13 : -1.53E-006 2.94E-007 0.000 0.3212 0.9000 0.9000   0.38  2  2  1.3E-003
 14 :  3.29E-007 1.08E-007 0.000 0.3680 0.9000 0.9000   0.51  2  2  2.7E-006
 15 :  2.43E-007 3.32E-008 0.000 0.3067 0.9000 0.9000   0.69  2  3  9.2E-007
 16 : -3.15E-008 7.28E-009 0.000 0.2191 0.9000 0.9000   0.98  3  3  3.6E-005
 17 : -1.07E-008 1.40E-009 0.000 0.1924 0.9000 0.9000   1.16  7  9  1.1E-005
 18 : -2.18E-009 3.16E-010 0.000 0.2254 0.9000 0.9000   1.05 15 14  2.3E-006
 19 : -3.89E-010 8.12E-011 0.000 0.2575 0.9000 0.9000   1.00 42 44  4.1E-007
 20 : -5.99E-011 2.36E-011 0.000 0.2900 0.9000 0.9000   0.98 35 39  6.4E-008
 21 : -1.53E-011 5.90E-012 0.000 0.2504 0.9000 0.9000   1.00 51 48  1.6E-008
Run into numerical problems.

iter seconds digits       c*x               b*y
 21      3.6  12.4  0.0000000000e+000 -1.5282564846e-011
|Ax-b| =  6.3e-009, [Ay-c]_+ =  2.8E-011, |x|= 3.2e+002, |y|= 4.5e+000

Detailed timing (sec)
   Pre          IPM          Post
1.270E-001    3.607E+000    3.800E-002    
Max-norms: ||b||=9.164989e+000, ||c|| = 0,
Cholesky |add|=15, |skip| = 0, ||L.L|| = 4.81323e+007.
sol = 
    yalmiptime: 8.1750
    solvertime: 3.7760
          info: 'No problems detected (SeDuMi-1.3)'
       problem: 0
        dimacs: [6.2007e-010 0 0 2.5642e-011 1.5283e-011 4.0466e-009]
monos = 
  Columns 1 through 6
    [8x4 sdpvar]    [8x4 sdpvar]    [8x4 sdpvar]    [12x4 sdpvar]    [8x4 sdpvar]    [8x4 sdpvar]
  Columns 7 through 8
    [27x9 sdpvar]    [24x8 sdpvar]
Q0 = 
  Columns 1 through 6
    [8x8 double]    [8x8 double]    [8x8 double]    [12x12 double]    [8x8 double]    [8x8 double]
  Columns 7 through 8
    [27x27 double]    [24x24 double]

>> double(X0)
ans =
    0.9803   -0.0625   -3.7728    1.2997
   -0.0625    1.0406   -0.2541   -6.2967
   -3.7728   -0.2541   34.4667  -12.4251
    1.2997   -6.2967  -12.4251   44.7506

>> double(X1)
ans =
   -0.1661    0.0634    1.8754   -1.3705
    0.0634   -0.1877    1.0337    0.5786
    1.8754    1.0337  -30.8065   12.6232
   -1.3705    0.5786   12.6232  -10.9368

>> double(F0)
ans =
   -0.8271    1.7957   -2.0447   -6.4058

>> double(F1)
ans =
    0.3876   -0.4929   -7.3939    1.3236
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